I'm trying to understand the easiest way to mix cement for the non-refractory areas of my oven structure. Can I use Quikrete with just water? Bread Builders and most other things I read all talk about mixing cement with sand, aggregate, etc. I don't mind mixing, I'm just trying to figure out what I need to buy. And is this the same for mortar and the solid concrete hearth slab?

Cement is a component of concrete. Concrete is the structural building material you'll use for your oven foundation and support slabs that typically includes sand, gravel and portland cement in addition to any fortifiers, water reducers, etc.
Designing ones' own concrete mix using these individual elements is done, but isn't necessary for this application. For a foundation and hearth slab, you'll get as good or better a final product using a bagged mix.

Quickrete is a bagged, premixed product. I wouldn't say that mixing and placing a slab via this route is "easy" but it's about as inexpensive as you'll get.
If you've consulted the Pompeii oven build instructions, you'll see that the block stand is dry-stacked vs. mortared, so the only thing you'd be using mortar for is your actual oven dome, and in that case, it's refractory mortar which can be purchased as a bagged pre-mix or "homebrewed" using the recipe found here.

Like lwood says, Heatstop is prohibitively expensive. At one point, when originally sourcing refractory mortar and could find no local HeatStop carriers, I called the HeatStop corp office to get the name of a local retailer and/or shipping costs. The lady on the other end of the line acted as if she was doing me a favor talking to me and was clear in her tone that she had much better things to do than answer my questions.

A great many builders (and me) have had success with the homebrew mortar, reportedly with less cracking than HeatStop. It is also recommended here that you stay away from the wet, premixed 'white glue' mortars.

If using HeatStop, stay away from the wet HeatStop II, what you want is the dry HeatStop 50. I don't know that it is prohibitively expensive, but like all refractory mortars, it isn't cheap. I paid $55 a bag and used 1 3/4. Still have at least 12 or 15 lbs left that I use for touch ups in my inner arch. If budget is an issue go with the homebrew, folks are having alot more success with it now than when I built my oven 4 yrs ago.

You'll need silica sand and fire clay for your mortar. Silica sand comes in mesh sizes from 30 to 200. I've used 60 and 120 with equal success. Fire clay comes in powder form in bags. It is also known as mortar clay and masons clay. You'll need a bag of lime and some Portland cement.

Here's a suggestion: Mix the parts dry in small amounts and place in a bucket for future use. I used a one pound coffee can as a measure. I found it easier to mix the dry ingredients by putting them on a sieve screen placed over a bucket then shake to blend the materials as they drop into the bucket. Pour the contents into another bucket a couple times to assure even blending. Wear a dust mask.

Poor man's mortar is one part Portland cement, one part fire clay, one part lime and three parts silica sand. 1:1:1:3. If you wish you can use 1/2 part lime instead of a full part. Mix the mortar thoroughly with water in small amounts, enough to do 6-8 bricks at a time. You can add a little water and remix if the mortar starts to thicken before you've used all of it. Eventually you learn and will know from a little experience how stiff to make the mix and how much you need to make at one time.

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